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| 研究生： |
許美中 |
|---|---|
| 論文名稱： |
實驗設計中可旋轉設計之研究 無 |
| 指導教授： | 柯阿銀 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 1982 |
| 畢業學年度： | 70 |
| 語文別： | 中文 |
| 論文頁數： | 106 |
| 中文關鍵詞： | 無 |
| 相關次數： | 點閱：117 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
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目錄
第一章 緒論1
第二章 基本可旋轉設計模式之建立5
第一節 具有意義的實驗範圍5
第二節 可旋轉設計及其成立之條件6
第三節 最小偏誤模式配置的合適性12
第四節 模式配置之檢定18
第三章 利用變換群建立二、三階可旋轉設計模式25
第一節 三維空間二階模式之設計25
第二節 三維以上空間二階模式之設計33
第三節 三維空間三階模式之設計39
第四節 四維空間三階模式之設計47
第四章 K維空間二階可旋轉模式之設計53
第一節 Draper之方法53
第二節 Herzberg之方法56
第三節 二者之比較59
第五章 由BIB設計建立二、三階可旋轉模式61
第一節 當r=3λ時，二階模式之設計61
第二節 當r≠3λ時，二階模式之設計63
第三節 三階模式之設計65
第六章 可旋轉設計之推廣73
第一節 圓柱狀可旋轉設計成立之條件73
第二節 圓柱狀可旋轉設計與可旋轉設計之比較77
第三節 三種圓柱狀可旋轉設計及其例示79
第四節 可分群體旋轉設計成立之條件84
第五節 四種基本可分群體旋轉設計建立方法85
第七章 結論89
附錄一91
附錄二94
參考書目100
參考書目
1. Cochran. W.G. and Cox, G.M. Experimental Designs, John Wiley & Sons, New York, 2nd Edition ,1968.
2. John, P.W.M. Statistical Design and Analysis of Experiments, Macmillan, New York, 1st edition, 1971.
3. Myers, R. Response Surface Methodology, Allyn and Bacon, Boston, Massachusetts, 1st edition,1971.
4. Bose, R.C. and Draper, N.R., “ Second order rotatable designs in three dimensions, “Ann. Math. Stat., 30, 1959, pp.1097-1112.
5. Box, G.E.P. and Wilson, K.B.,” On the experimental attainment of optimum conditions,” J.R.S.S. series B,13, 1951, pp.1-45.
6. Box, G.E.P. and Hunter. J.S.,”Multi-factor experimental designs for exploring response
surfaces,”Ann. Math. Stat., 28, 1957, pp.195-241.
7. Box, G.E.P.,”Multifactor Designs of first order,” Biometrika, 30, 1952, pp.49-57.
8. Box, G.E.P. and Draper, N.R., “The choice of a second order rotatable design,” Biometrika, 50, 1963, pp.335-352.
9. Box, G.E.P. and Behnken, V.W.,” Simplex-sum designs：a class of second order rotatable designs derivable from those of first order, “Ann, Maths.Stat. 31, 1960, pp.838-864.
10. Box, G. E. P. and Behnken D.W., “Some new three level designs for the study of quantitative variables,” Technometrics, 2, 1960, pp.455-475.
11. Draper, N.R., “Third order rotatable designs in three dimensions, “Ann. Math. Stat., 31. 1960, pp. 865- 874.
12. De Baun, R.M., “Response surface designs for three factors at three levels, “Technometrics, 1, 1959, pp. 1 - 8.
13. Draper, N.R., “Third order rotatable designs in three dimensions : some specific designs,” Ann. Math. Stat., 32, 1961, pp.910-913.
14.Draper, N.R., “Third order rotatable dosigns in three factors：Analysis, “Technometrics, 4, 1962,pp.219- 234.
15. Das, M.N. and Narasimham. V.L.,”Construction of rotatable designs through balanced incomplete block designs,” Ann. Math. Stat., 33, 1962,pp. 1421- 1439.
16. Draper, N.R., “ A third order rotatable design in four dimensions,” Ann. Math. stat., 31, 1960,pp.875-877.
17. Das, M.N. and Dey, A..”Group-divisible rotatable designs,” Ann. Inst. Stat. Math., 19, 1967, pp.331-347.
18. Dey A. and Nigam A. K., “Group divisible rotatable designs-some further considerations,” Ann. Inst. Stat. Math., 20, 1968, pp.477-481.
19. Draper, N.R., “Second order rotatable designs in four or more dimensions,” Ann. Math. Stat., 31,1960, pp.23-33.
20.Gardiner, D.A., Grandage, A.H.E. and Hader, R.J., “Third order rotatable designs for exploring response surfaces,”Ann. Math. Stat., 30, 1959., pp. 1082- 1096.
21.Herzberg, A.M.,”Cylindrically rotatable designs, “Ann. Math. Stat., 37, 1966, pp,242-247.
22. Herzberg, A.M., “Cylindrically rotatable designs of type 1, 2, and 3, “Ann. Maths Stat., 38, 1967, pp.167-176.
23. Herzberg, A.M., “ Two third order rotatable designs in four dimensions, “Ann. Math. Stat., 35, 1964. pp.445-446.
24. Herzberg , A.M,, “A method for the construction of second order rotatable designs in k dimensions,” Ann. Math.Stat., 38, 1967, pp.177-180.
25. Karson, M.J., Manson, A.R. and Hader, R.J., “Minimum bias estimation and experimental design for response surfaces,” Technometrics, 11, 1969, pp.461-475.
26. Lipow P., Draper N.R., and Guttman I.,”All-bias designs for spline functions joined at the axes,”J.A.S.A., 72, 1977, pp.424-429.
27.Manson, A.R. and Evans, J.W.,” Optimal experimental designs in two dimensions using minimum bias estimation, “ JASA, 73, 1978, pp.171-176.
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